Determine the quadrant in which an angle, θ, lies if θ = 5.40 radians.
a. 4th quadrant
b. 3rd quadrant
c. 2nd quadrant
d. 1st quadrant
5.4 radians
coterminal with 5.4 - 2π
= -.883.. radians, which is in the IV th
or if you want to "think" in degrees
1 rad = 180/π °
5.4 rad = 309.39.. ° ----> 4th
i like turtlws
Well, let me tell you a little joke before I answer your question:
Why did the angle go to the hospital?
Because it had a radian-t infection! 😄
Now, coming back to your question, an angle of 5.40 radians lies in the 2nd quadrant. So, the correct answer is c. 2nd quadrant.
To determine the quadrant in which an angle θ lies, we can use the following guidelines:
1. In the 1st quadrant, both the x-coordinate and the y-coordinate are positive.
2. In the 2nd quadrant, the x-coordinate is negative and the y-coordinate is positive.
3. In the 3rd quadrant, both the x-coordinate and the y-coordinate are negative.
4. In the 4th quadrant, the x-coordinate is positive and the y-coordinate is negative.
Now, let's determine the quadrant in which an angle θ = 5.40 radians lies:
Since radians measure the rotation from the x-axis in a counterclockwise direction, we can determine the quadrant by considering the location of the terminal side of the angle.
Since θ = 5.40 radians, we can see that the angle has finished more than one full rotation (2π = 6.28 radians), but it hasn't reached the second rotation.
Therefore, the terminal side of the angle θ = 5.40 radians lies in the 1st quadrant.
The answer is: d. 1st quadrant.
To determine in which quadrant an angle θ lies, we need to look at the value of θ in radians and consider the positive or negative x and y coordinates.
In this case, θ = 5.40 radians.
A full circle or revolution in radians is equal to 2π radians. So, we can say that 2π radians is equivalent to 360 degrees.
To determine the quadrant, we need to determine the reference angle, which is the angle formed between the terminal side of θ and the x-axis.
To find the reference angle, we subtract the closest multiple of π (180 degrees) from θ. In this case, the closest multiple of π to 5.40 radians is 6 radians.
Reference angle = θ - (nearest multiple of π)
Reference angle = 5.40 radians - 6 radians
Reference angle = -0.60 radians
Now, we need to look at the sign of the x and y coordinates in each quadrant to determine where the angle lies.
In the 1st quadrant, both x and y coordinates are positive.
In the 2nd quadrant, x coordinate is negative, and y coordinate is positive.
In the 3rd quadrant, both x and y coordinates are negative.
In the 4th quadrant, x coordinate is positive, and y coordinate is negative.
Since the reference angle is negative (-0.60 radians), we can conclude that the angle θ lies in the 4th quadrant.
Therefore, the answer is a. 4th quadrant.